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Date: Thu, 7 Jul 2016 01:28:54 0400
Subject: [PATCH] books/bookvolbib Axiom Citations in the Literature
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Goal: Axiom Literate Programming
index{Caruso, Fabrizio}
\begin{chunk}{axiom.bib}
@misc{Caru10,
author = "Caruso, Fabrizio",
title = "Factorization of NonCommutative Polynomials",
url = "https://arxiv.org/pdf/1002.3108.pdf",
paper = "Caru10.pdf",
keywords = "axiomref",
year = "2010",
abstract =
"We describe an algorithm for the factorization of noncommutative
polynomials over a field. The first sketch of this algorithm appeared
in an unpublished manuscript (literally hand written notes) by James
H. Davenport more than 20 years ago. This version of the algorithm
contains some improvements with respect to the original sketch. An
improved version of the algorithm has been fully implemented in the
Axiom computer algebra system."
}
\end{chunk}
\index{Chen, Changbo}
\index{Davenport, James H.}
\index{May, John P.}
\index{Maza, Marc Moreno}
\index{Xia, Bican}
\index{Xiao, Rong}
\begin{chunk}{axiom.bib}
@misc{Chen10,
author = "Chen, Changbo and Davenport, James H. and May, John P. and
Maza, Marc Moreno and Xia, Bican and Xiao, Rong",
title = "Triangular Decomposition of Semialgebraic Systems",
year = "2010",
url = "https://arxiv.org/pdf/1002.4784.pdf",
paper = "Chen10.pdf",
abstract =
"Regular chains and triangular decompositions are fundamental and
welldeveloped tools for describing the complex solutions of
polynomial systems. This paper proposes adaptations of these tools
focusing on solutions of the real analogue: semialgebraic systems.
We show that any such system can be decomposed into finitely many
regular semialgebraic systems. We propose two specifications of such
a decomposition and present corresponding algorithms. Under some
assumptions, one type of decomposition can be computed in singly
exponential time w.r.t. the number of variables. We implement our
algorithms and the experimental results illustrate their
effectiveness."
}
\end{chunk}
\index{Certik, Ondrej}
\begin{chunk}{axiom.bib}
@misc{Cert16,
author = "Certik, Ondrej",
title = "SymPy vs. Axiom",
url = "https://github.com/sympy/sympy/wiki/SymPyvs.Axiom",
keywords = "axiomref"
}
\end{chunk}
\index{Baker, Martin}
\begin{chunk}{axiom.bib}
@misc{Bake16a,
author = "Baker, Martin",
title = "Axioms in Axiom",
keywords = "axiomref",
year = "2016",
url = "http://www.euclideanspace.com/prog/scratchpad/axiomsinAxiom"
}
\end{chunk}
\index{Joyner, W. D.}
@misc{Joyn08,
author = "Joyner, W. D.",
title = "Open Source Mathematical Software: A White Paper",
url = "http://wdjoyner.com/writing/research/oscasnsfwhitepaper12.tex",
paper = "Joyn08.tex",
keywords = "axiomref",
year = "2008"
}
\index{Karpinski, Stefan}
\begin{chunk}{axiom.bib}
@misc{Karp14,
author = "Karpinski, Stefan",
title = "Re: Symbolic Math: try a translation of Axiom to Julia?",
url =
"https://groups.google.com/forum/#!msg/juliadev/NTfS9fJuIcE/MINQuQuGfoUJ",
keywords = "axiomref",
year = "2016"
}
\end{chunk}
\begin{chunk}{axiom.bib}
@misc{America,
author = "america.pink",
title = "Axiom (computer algebra system)",
year = "2016",
keywords = "axiomref",
url = "http://america.pink/axiomcomputeralgebrasystem_526647.html"
}
\end{chunk}
\index{Davenport, James H.}
\index{Siret, Y.}
\index{Tournier, E.}
\begin{chunk}{axiom.bib}
@book{Dave88,
author = "Davenport, James H. and Siret, Y. and Tournier, E.",
title =
"Computer Algebra: Systems and Algorithms for Algebraic Computation",
publisher = "Academic Press",
year = "1988",
isbn ="0122042329",
url = "http://staff.bath.ac.uk/masjhd/masternew.pdf",
paper = "Dave88.pdf",
keywords = "axiomref",
abstract =
"The need for a good general text on Computer Algebra has never been
greater. From the very beginning, computers have been used for
numerical calculation. It is not always realized however that their
use for mathematical calculation of a symbolic nature has a history
almost as long. It is only recently that improvement in algorithms,
the development of small systems and the emergence of powerful
workstations have combined to make Computer Algebra systems much more
widely available and an increasingly important tool for almost all
users of Mathematics. Part of the reason why Computer Algebra was for
so long something of an esoteric discipline, has surely been the lack
of textbooks on the subject. The arrival of the present volume on the
scene has thus been particularly fortunate.
The approach adopted by the authors is to begin by giving the reader
an idea of the sort of calculations that Algebra Systems can
perform. Next the questions of data representation are
treated. Finally the bulk of the book is devoted to explaining the
classical algorithms of the subject. The reader is thereby given both
a feel for the problems, such as data representation and combinatorial
explosion, that system designers need to face, and a general
understanding of the underlying Mathematics. The book is not intended
to provide encyclopedic coverage, nor is it meant to be serve as a
manual for any particular system.
One of the more difficult design decisions facing authors of such a
book concerns the level of mathematical sophistication to be assumed
on behalf of the reader. One wants the book to be accessible to as
wide an audience as possible, but any understanding of the subject
beyond the more superficial requires a reasonable grasp of the
underlying Pure Mathematics. The compromise made in the present text
is to fully explain the mathematical problems, to state the theorems
and consequent algorithms, but not always to prove the theorems. Many
of the more straightforward results are proved though. The decisions
as to what to include and what to omit have been well thought out and
the result is a considerable success. The book has a great deal to
offer engineers and scientists and its early chapters in particular
could most suitably serve as the basis for an undergraduate
course. For the professional mathematician it provides a good quick
allround introduction to a fascinating and rapidly evolving area.
Of course in a book such as this, not everything that might fall under
the umbrella of Computer Algebra can be covered. Thus some specialized
topics, such as Computational Group Theory, are not mentioned, and the
treatment of other areas is sometimes necessarily abbreviated. However
the main stream of the subject is well represented, and the selection
of material generally well judged. Typically, the main classical
results are fully explained, some of the more interesting developments
and variations are sketched, and the reader is referred to the
standard literature of the subject for further details.
The first chapter is entitled ``How to use a Computer Algebra
System''. Here the reader is led through a session with the MACSYMA
system obtaining a vicarious handson experience. Beginners would be
well advised to follow the authors’ suggestion and duplicate the
session on their local system as closely as possible. The examples
chosen are interesting, though perhaps a little too ‘pure
mathematical’ for some tastes. Overall the chapter gives a good idea
of the capabilities of algebra systems.
Chapter 2 is concerned with the representation of the various
mathematical quantities which algebra systems handle. It might be
thought that data repesentation is mainly a computerscience matter,
but in fact some rather interesting mathematical problems concerning
uniqueness arise. The chapter includes, among other things, discussion
of the non modular methods for computing gcds (the subresultant
algorithm for example), the handling of algebraic quantities the Risch
Structure Theorem and the Bareiss Method of Gaussian elimination.
The third chapter treats two major topics under the heading
``Polynomial Simplification''. Firstly there is a concise, but good,
explanation of Buchberger’s Groebnerbasis methods for computations in
polynomial rings. Secondly there is an equally good introduction to
the use of cylindrical decomposition for obtaining approximations to
real roots of polynomial equations.
Chapter 4, which is headed ``Advanced Algorithms'', begins with a
discussion of modular methods, in particular the modular gcd. A brisk
treatment of the Berlekamp factorization method follows, together with
both the linear and quadratic varieties of the Hensel Lemma. In
addition there is a short section on the factorization of polynomials
in several variables. In general the high standard of the book is
maintained, but, unusually, the treatment of the modular gcd suffers a
little from typos and the explanation of the Hensel Lemma could be
clearer in places.
The major part of the final chapter is devoted to symbolic integration
and related topics concerning the formal solution of some ordinary
differential equations. These form the ‘high point’ of the book. Here
in particular the reader is led to the borders of current
research. The final part of Chapter 5 is concerned with asymptotic
expansions of solutions of differential equations. I found the
treatment of this topic too brief to be entirely successful. Those
already familiar with the theory of asymptotic expansion will no doubt
be interested in the details of the implementation, but the beginner
needs a fuller treatment, which this important topic surely deserves.
The book also contains an appendix and an annex. The former is
entitled ``Algebraic Background''. It is useful to refer to, but would
not be sufficient for anyone whose background did not already include
a fair familiarity with most of its contents. The annex contains a
description of the REDUCE system. Here the reader is able to see how
some of the algorithms described in the main part of the book are used
in an actual system.
The bibliography is excellent, though I do have two minor carps. One
or two articles mentioned in the text do not appear in the
bibliography, Also inclusion of one or two ‘standard’ mathematical
works, and appropriate reference to them in the text, would make the
book more accessible to people whose main speciality is not
Mathematics.
The few minor quibbles I have with this book are of little
importance. It provides an excellent introduction to Computer
Algebra. At the time of writing, it is still, to the best of my
knowledge, the only general textbook on the subject and it is indeed
fortunate that it is such a good one.
The second edition incorporates many recent advances in theory and
practice of computer algebra (a short proof of the convergence of
Buchberger’s algorithm as well as recent releases of software
described in the text). Further a description of the AXIOM system is
included.
This book definitely represents one of the best introductions to
computer algebra accessible to beginners and researchers."
}
\end{chunk}
\index{Heck, Andre}
\begin{chunk}{axiom.bib}
@book{Heck93,
author = "Heck, Andre",
title = "Introduction to Maple",
year = "1993",
publisher = "SpringerVerlag",
keywords = "axiomref",
abstract =
"This is an introductory book on one of the most powerful computer
algebra systems, viz, Maple: The primary emphasis in this book is on
learning those things that can be done with Maple and how it can be
used to solve mathematical problems. In this book usage of Maple as a
programming language is not discussed at a higher level than that of
defining simple procedures and using simple language constructs.
However, the Maple data structures are discussed in detail.
This book is divided into eighteen chapters spanning a variety of
topics. Starting with an introduction to symbolic computation and
other similar computer algebra systems, this book covers several
topics like polynomials and rational functions, series,
differentiation and integration, differential equations, linear
algebra, 2D and 3D graphics, etc. The applications covered include
kinematics of the Stanford manipulator, a 3component model for
cadmium transfer through the human body, molecularorbital Hückel
theory, prolate spheroidal coordinates and MoorePenrose inverses.
At the end of each chapter, a good number of excercises is given. A
list of relevant references is also given at the end of the book.
This book is very useful to all users of Maple package."
}
\end{chunk}
\index{Lazard, Daniel}
\begin{chunk}{axiom.bib}
@InProceedings{Laza93,
author = "Lazard, Daniel",
title = "On the representation of rigidbody motions and its application
to generalized platform manipulators",
booktitle = "Proc. Workshop Computational Kinematics",
year = "1993",
location = "Dagstuhl Castle, Germany",
publisher = "Kluwer Academic Publishers",
pages = "175181",
keywords = "axiomref",
abstract =
"Different ways for representing rigid body motions (direct isometries)
by a computer are presented. It turns out that the choice between them
may have a dramatic effect on the difficulty of a computation or of a
proof. As an application, a computational proof is given of the fact
that the direct kinematic problem for the generalized Stewart platform
has at most 40 complex solutions."
}
\end{chunk}
\index{Mishra, Bhubaneswar}
\begin{chunk}{axiom.bib}
@book{Mish93,
author = "Mishra, Bhubaneswar",
title = "Algorithmic Algebra",
publisher = "SpringerVerlag",
series = "Texts and Monographs in Computer Sciences",
year = "1993",
keywords = "axiomref",
abstract =
"This book is based on a graduate course in computer science taught in
1987. The following topics are covered: computational ideal theory,
solving systems of polynomial equations, elimination theory, real
algebra, as well as an introduction chapter and two chapters with the
needed algebraic background. The book is selfcontained and the proofs
are given with many details.
It is clear that this book is only an introduction to the topic and
does not cover the many improvements that appeared in the last 7 years
about for example the computation of Groebner basis, polynomial
solving, multivariate resultants and algorithms in real
algebra. Choices had to be made to keep the content of a reasonable
size and the complexity issues are not considered.
The choice of topics is excellent, there are many exercises and
examples. It is a very useful book."
}
\end{chunk}
\index{Scheerhorn, Alfred}
\begin{chunk}{axiom.bib}
@misc{Sche93,
author = "Scheerhorn, Alfred",
title = "Presentation of the algebraic closure of finite fields and
tracecompatible polynomial sequences",
comment = "Darstellungen des algebraischen Abschlusses endlicher Korper
und spurkompatible Polynomfolgen",
year = "1993",
keywords = "axiomref",
abstract =
"For numerical experiments concerning various problems in a finite
field $\mathbb{F}_q$ it is useful to have an explicit data
presentation $\mathbb{F}_{q^m}$ of for large $m$, and a method for the
construction of towers
\[\mathbb{F}_q \subset \mathbb{F}_{q^{d_1}} \subset \cdots \subset
\mathbb{F}_{q^{d_k}} = \mathbb{F}_{q^m}\]
In order to avoid the identification problem it is advantageous to
have all fields in the tower presented by properly chosen normal bases,
whereby the embedding
$\mathbb{F}_{q^{d_i}} \subset \mathbb{F}_{q^{d_{i+1}}}$
is given by the trace function.
The following notion is introduced: A sequence of polynomials
$\{f_n  n \ge 1\}$ with degree$(f_n)=n$ called tracecompatible over
$\mathbb{F}_q$ if (1) $f_n$ is a normal polynomial over $\mathbb{F}_q$,
(2) if $\alpha_n \in \mathbb{F}_{q^n}$ is a root of $f_n$, then for any
proper divisor $d$ of $n$ the trace of $\alpha_n$ over $\mathbb{F}_{q^d}$
is a root of $f_d$.
The main goal of the dissertation is to give algorithms for
construction of sequences of tracecompatible polynomials and to
present explicit numerical data. An analogous notion of
normcompatible sequences is also introduced and studied.
The dissertation consists of four chapters and a supplement, as
follows: (1) Basic notions (131). (2) Presentation of the algebraic
closure of a finite field (3259). (3) Sequences of polynomials and
sequences of elements (60115). (4) Implementations (118139). (5)
Supplement (142171).
In chapters (1)–(3) various known results and algorithms are
collected, and new results are added and compared with those
previously used.
The numerical results in the supplement contain sequences of
tracecompatible polynomials of degree $n$, where $n \le 100$, and
$q=2,3,5,7,11,13$. For implementation, the computeralgebra system
AXIOM has been used. The details contained in this dissertation are
not readily describable in a short review."
}
\end{chunk}
\index{Singer, Michael F.}
\index{Ulmer, Felix}
\begin{chunk}{axiom.bib}
@article{Sing93,
author = "Singer, Michael F. and Ulmer, Felix",
title = "Galois groups of second and third order linear differential
equations",
journal = "J. Symb. Comput.",
volume = "16",
number = "1",
pages = "936",
year = "1993",
keywords = "axiomref",
paper = "Sing93.pdf",
abstract =
"The authors discuss the first problem of Galois theory of differential
equations. Let $F$ be an ordinary (for simplicity) differential field
and $L(y)=0$ be an ordinary linear differential equation over $F$. How
can one calculate the Galois group of $L$ over $F$? The authors
suppose a new approach to the problem. They reduce it to the problem
of finding solutions of linear differential equations in $F$ and to
the factorization problem of such equations over $F$. These allow them
to give simple necessary and sufficient conditions for a second order
linear differential equation to have Liouvillian solutions and for a
third order linear differential equation to have Liouvillian solutions
or to be solvable in terms of second order equations."
}
\end{chunk}
\index{Singer, Michael F.}
\index{Ulmer, Felix}
\begin{chunk}{axiom.bib}
@article{Sing93a,
author = "Singer, Michael F. and Ulmer, Felix",
title = "Liouvillian and algebraic solutions of second and third order
linear differential equations",
journal = "J. Symb. Comput.",
volume = "16",
number = "1",
pages = "3773",
year = "1993",
paper = "Sing93a.pdf",
keywords = "axiomref",
abstract =
"Let $F$ be an ordinary differential field of characteristic 0 and
$L \in F $ be a linear homogeneous polynomial. How can one find the
Liouvillian solutions of $L(y)=0$? In the paper this problem is
reduced to the problems of (1) factorization and (2) finding $u$
solutions such that $\frac{u^{\prime}}{y} \in F$ of $L$ and some
polynomials associated with it (symmetric powers of $L$).
Now there are the algorithms for the solution of the last problems for
$F=\mathbb{Q}(x)$ [see D. Yu. Grigor’ev, J. Symb. Comput. 10, 737
(1990; Zbl 0728.68067) and M. F. Singer, Am. J. Math. 103, 661682
(1981; Zbl 0477.12026)].
For polynomials $L$ of the second and third order the authors provide
full investigation of the most difficult case when the solution $u$ of
$L(y)$ is algebraic. They show that one can compute the minimal
polynomial $P(y) \in F[y]$ of $u$. We note that the authors
essentially used the tools of representation theory, invariant theory
and computer algebra."
}
\end{chunk}
\index{Smith, Geoff C.}
\begin{chunk}{axiom.bib}
@article{Smit93,
author = "Smith, Geoff C.",
title = "Group theory results with machine generated proofs",
journal = "An. Univ. Timis., Ser. Mat.Inform.",
volume = "31",
number = "2",
pages = "273280",
year = "1993",
keywords = "axiomref",
abstract =
"There are a variety of theorems in group theory which admit of proofs
by machine. This talk illustrates these techniques in action. Examples
are given of this phenomenon, drawn from the theory of group
presentations, and from the theory of $p$groups. The systems involved
include AXIOM, CAYLEY and QUOTPIC"
}
\end{chunk}
\index{Geddes, K. O.}
\index{Czapor, S.R.}
\index{Labahn, George}
\begin{chunk}{axiom.bib}
@book{Gedd92,
author = "Geddes, Keith and Czapor, O. and Stephen R. and Labahn, George",
title = "Algorithms For Computer Algebra",
year = "1992",
publisher = "Kluwer Academic Publishers",
isbn = "0792392590",
month = "September",
year = "1992",
keywords = "axiomref",
abstract =
"Computer Algebra (CA) is the name given to the discipline of
algebraic, rather than numerical, computation. There are a number of
computer programs – Computer Algebra Systems (CASs) – available for
doing this. The most widely used generalpurpose systems that are
currently available commercially are Axiom, Derive, Macsyma, Maple,
Mathematica and REDUCE. The discipline of computer algebra began in
the early 1960s and the first version of REDUCE appeared in 1968.
A large class of mathematical problems can be solved by using a CAS
purely interactively, guided only by the user documentation. However,
sophisticated use requires an understanding of the considerable amount
of theory behind computer algebra, which in itself is an interesting
area of constructive mathematics. For example, most systems provide
some kind of programming language that allows the user to expand or
modify the capabilities of the system.
This book is probably the most general introduction to the theory of
computer algebra that is written as a textbook that develops the
subject through a smooth progression of topics. It describes not only
the algorithms but also the mathematics that underlies them. The book
provides an excellent starting point for the reader new to the
subject, and would make an excellent text for a postgraduate or
advanced undergraduate course. It is probably desirable for the reader
to have some background in abstract algebra, algorithms and
programming at about secondyear undergraduate level.
The book introduces the necessary mathematical background as it is
required for the algorithms. The authors have avoided the temptation
to pursue mathematics for its own sake, and it is all sharply focused
on the task of performing algebraic computation. The algorithms are
presented in a pseudolanguage that resembles a cross between Maple
and C. They provide a good basis for actual implementations although
quite a lot of work would still be required in most cases. There are
no code examples in any actual programming language except in the
introduction.
The authors are all associated with the group that began the
development of Maple. Hence, the book reflects the approach taken by
Maple, but the majority of the discussion is completely independent of
any actual system. The authors’ experience in implementing a practical
CAS comes across clearly.
The book focuses on the core of computer algebra. The first chapter
introduces the general concept and provides a very nice historical
survey. The next three chapters discuss the fundamental topics – data
structures, representations and the basic arithmetic of integers,
rational numbers, multivariate polynomials and rational functions – on
which the rest of the book is built.
A major technique in CA involves projection onto one or more
homomorphic images, for which the ground ring is usually chosen to be
a finite field. The image solution is lifted back to the original
problem domain by means of the Chinese Remainder Theorem in the case
of multiple homomorphic images, or the Hensel (adic or idealadic)
construction in the case of a single image. The next two chapters are
devoted to these techniques in a fairly general setting. The two
subsequent chapters specialise them to GCD computation and
factorisation for multivariate polynomials; the first of these
chapters also discusses the important but difficult topic of
subresultants.
The next two chapters describe the use of fractionfree Gaussian
elimination, resultants and Gröbner Bases for manipulation and exact
solution of linear and nonlinear polynomial equations. The two final
chapters describe ``classical'' algorithms and the more recent Risch
algorithm for symbolic indefinite integration, and provide an
introduction to differential algebra.
The book does not consider more specialised problem areas such as
symbolic summation, definite integration, differential equations,
group theory or number theory. Nor does it consider more applied
problem areas such as vectors, tensors, differential forms, special
functions, geometry or statistics, even though Maple and other CASs
provide facilities in all or many of these areas. It does not consider
questions of CA programming language design, nor any of the important
but nonalgebraic facilities provided by current CASs such as their
user interfaces, numerical and graphical facilities.
This is a long book (nearly 600 pages); it is generally very well
presented and the three authors have merged their contributions
seamlessly. I noticed very few typographical errors, and none of any
consequence. I have only two complaints about the book. The typeface
is too small, particularly for the relatively large line spacing used,
and it is much too expensive, particularly for a book that would
otherwise be an excellent student text. I recommend it highly to
anyone who can afford it."
}
\end{chunk}

books/bookvolbib.pamphlet  623 +++++++++++++++++++++++++++++
changelog  2 +
patch  813 +++++++++++++++++++++++++
src/axiomwebsite/patches.html  2 +
4 files changed, 1108 insertions(+), 332 deletions()
diff git a/books/bookvolbib.pamphlet b/books/bookvolbib.pamphlet
index e39c1ba..e49382b 100644
 a/books/bookvolbib.pamphlet
+++ b/books/bookvolbib.pamphlet
@@ 3,6 +3,7 @@
\input{bookheader.tex}
\mainmatter
\setcounter{chapter}{0} % Chapter 1
+% See: http://www.swmath.org/software/63
\chapter{The Axiom Bibliography}
This bibliography covers areas of computational mathematics.
Papers which mention Axiom have a ``keyword='' entry of ``axiomref''.
@@ 10115,6 +10116,37 @@ J. Symbolic Computation 5, 237259 (1988)
\end{chunk}
\index{Chen, Changbo}
+\index{Davenport, James H.}
+\index{May, John P.}
+\index{Maza, Marc Moreno}
+\index{Xia, Bican}
+\index{Xiao, Rong}
+\begin{chunk}{axiom.bib}
+@misc{Chen10,
+ author = "Chen, Changbo and Davenport, James H. and May, John P. and
+ Maza, Marc Moreno and Xia, Bican and Xiao, Rong",
+ title = "Triangular Decomposition of Semialgebraic Systems",
+ year = "2010",
+ url = "https://arxiv.org/pdf/1002.4784.pdf",
+ paper = "Chen10.pdf",
+ abstract =
+ "Regular chains and triangular decompositions are fundamental and
+ welldeveloped tools for describing the complex solutions of
+ polynomial systems. This paper proposes adaptations of these tools
+ focusing on solutions of the real analogue: semialgebraic systems.
+
+ We show that any such system can be decomposed into finitely many
+ regular semialgebraic systems. We propose two specifications of such
+ a decomposition and present corresponding algorithms. Under some
+ assumptions, one type of decomposition can be computed in singly
+ exponential time w.r.t. the number of variables. We implement our
+ algorithms and the experimental results illustrate their
+ effectiveness."
+}
+
+\end{chunk}
+
+\index{Chen, Changbo}
\index{Maza, Marc Moreno}
\begin{chunk}{axiom.bib}
@misc{Chen12,
@@ 11583,6 +11615,9 @@ J. Symbolic Computation 5, 237259 (1988)
\begin{chunk}{axiom.bib}
@misc{America,
+ author = "america.pink",
+ title = "Axiom (computer algebra system)",
+ year = "2016",
keywords = "axiomref",
url = "http://america.pink/axiomcomputeralgebrasystem_526647.html"
}
@@ 11890,6 +11925,18 @@ American Mathematical Society (1994)
\end{chunk}
+\index{Baker, Martin}
+\begin{chunk}{axiom.bib}
+@misc{Bake16a,
+ author = "Baker, Martin",
+ title = "Axioms in Axiom",
+ keywords = "axiomref",
+ year = "2016",
+ url = "http://www.euclideanspace.com/prog/scratchpad/axiomsinAxiom"
+}
+
+\end{chunk}
+
\index{Ballarin, Clemens}
\begin{chunk}{axiom.bib}
@article{Ball14,
@@ 12957,6 +13004,27 @@ Informatique et en Automatique, Le Chesnay, France, 12pp
\end{chunk}
+\index{Caruso, Fabrizio}
+\begin{chunk}{axiom.bib}
+@misc{Caru10,
+ author = "Caruso, Fabrizio",
+ title = "Factorization of NonCommutative Polynomials",
+ url = "https://arxiv.org/pdf/1002.3108.pdf",
+ paper = "Caru10.pdf",
+ keywords = "axiomref",
+ year = "2010",
+ abstract =
+ "We describe an algorithm for the factorization of noncommutative
+ polynomials over a field. The first sketch of this algorithm appeared
+ in an unpublished manuscript (literally hand written notes) by James
+ H. Davenport more than 20 years ago. This version of the algorithm
+ contains some improvements with respect to the original sketch. An
+ improved version of the algorithm has been fully implemented in the
+ Axiom computer algebra system."
+}
+
+\end{chunk}
+
\index{Caviness, Bob}
\index{Trager, Barry}
\index{Gianni, Patrizia}
@@ 13046,6 +13114,17 @@ Informatique et en Automatique, Le Chesnay, France, 12pp
\end{chunk}
+\index{Certik, Ondrej}
+\begin{chunk}{axiom.bib}
+@misc{Cert16,
+ author = "Certik, Ondrej",
+ title = "SymPy vs. Axiom",
+ url = "https://github.com/sympy/sympy/wiki/SymPyvs.Axiom",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
\index{Chicha, Yannis}
\index{Lloyd, Michael}
\index{Oancea, Cosmin}
@@ 13805,13 +13884,144 @@ Mathematical Sciences Department, IBM Thomas Watson Research Center 1984
\index{Davenport, James H.}
\index{Siret, Y.}
\index{Tournier, E.}
\begin{chunk}{ignore}
\bibitem[Davenport 88]{DST88} Davenport, J.H.; Siret, Y.; Tournier, E.
Computer Algebra: Systems and Algorithms for Algebraic Computation.
Academic Press, New York, NY, USA, 1988, ISBN 0122042329
+\begin{chunk}{axiom.bib}
+@book{Dave88,
+ author = "Davenport, James H. and Siret, Y. and Tournier, E.",
+ title =
+ "Computer Algebra: Systems and Algorithms for Algebraic Computation",
+ publisher = "Academic Press",
+ year = "1988",
+ isbn ="0122042329",
url = "http://staff.bath.ac.uk/masjhd/masternew.pdf",
 paper = "DST88.pdf",
+ paper = "Dave88.pdf",
keywords = "axiomref",
+ abstract =
+ "The need for a good general text on Computer Algebra has never been
+ greater. From the very beginning, computers have been used for
+ numerical calculation. It is not always realized however that their
+ use for mathematical calculation of a symbolic nature has a history
+ almost as long. It is only recently that improvement in algorithms,
+ the development of small systems and the emergence of powerful
+ workstations have combined to make Computer Algebra systems much more
+ widely available and an increasingly important tool for almost all
+ users of Mathematics. Part of the reason why Computer Algebra was for
+ so long something of an esoteric discipline, has surely been the lack
+ of textbooks on the subject. The arrival of the present volume on the
+ scene has thus been particularly fortunate.
+
+ The approach adopted by the authors is to begin by giving the reader
+ an idea of the sort of calculations that Algebra Systems can
+ perform. Next the questions of data representation are
+ treated. Finally the bulk of the book is devoted to explaining the
+ classical algorithms of the subject. The reader is thereby given both
+ a feel for the problems, such as data representation and combinatorial
+ explosion, that system designers need to face, and a general
+ understanding of the underlying Mathematics. The book is not intended
+ to provide encyclopedic coverage, nor is it meant to be serve as a
+ manual for any particular system.
+
+ One of the more difficult design decisions facing authors of such a
+ book concerns the level of mathematical sophistication to be assumed
+ on behalf of the reader. One wants the book to be accessible to as
+ wide an audience as possible, but any understanding of the subject
+ beyond the more superficial requires a reasonable grasp of the
+ underlying Pure Mathematics. The compromise made in the present text
+ is to fully explain the mathematical problems, to state the theorems
+ and consequent algorithms, but not always to prove the theorems. Many
+ of the more straightforward results are proved though. The decisions
+ as to what to include and what to omit have been well thought out and
+ the result is a considerable success. The book has a great deal to
+ offer engineers and scientists and its early chapters in particular
+ could most suitably serve as the basis for an undergraduate
+ course. For the professional mathematician it provides a good quick
+ allround introduction to a fascinating and rapidly evolving area.
+
+ Of course in a book such as this, not everything that might fall under
+ the umbrella of Computer Algebra can be covered. Thus some specialized
+ topics, such as Computational Group Theory, are not mentioned, and the
+ treatment of other areas is sometimes necessarily abbreviated. However
+ the main stream of the subject is well represented, and the selection
+ of material generally well judged. Typically, the main classical
+ results are fully explained, some of the more interesting developments
+ and variations are sketched, and the reader is referred to the
+ standard literature of the subject for further details.
+
+ The first chapter is entitled ``How to use a Computer Algebra
+ System''. Here the reader is led through a session with the MACSYMA
+ system obtaining a vicarious handson experience. Beginners would be
+ well advised to follow the authors’ suggestion and duplicate the
+ session on their local system as closely as possible. The examples
+ chosen are interesting, though perhaps a little too ‘pure
+ mathematical’ for some tastes. Overall the chapter gives a good idea
+ of the capabilities of algebra systems.
+
+ Chapter 2 is concerned with the representation of the various
+ mathematical quantities which algebra systems handle. It might be
+ thought that data repesentation is mainly a computerscience matter,
+ but in fact some rather interesting mathematical problems concerning
+ uniqueness arise. The chapter includes, among other things, discussion
+ of the non modular methods for computing gcds (the subresultant
+ algorithm for example), the handling of algebraic quantities the Risch
+ Structure Theorem and the Bareiss Method of Gaussian elimination.
+
+ The third chapter treats two major topics under the heading
+ ``Polynomial Simplification''. Firstly there is a concise, but good,
+ explanation of Buchberger’s Groebnerbasis methods for computations in
+ polynomial rings. Secondly there is an equally good introduction to
+ the use of cylindrical decomposition for obtaining approximations to
+ real roots of polynomial equations.
+
+ Chapter 4, which is headed ``Advanced Algorithms'', begins with a
+ discussion of modular methods, in particular the modular gcd. A brisk
+ treatment of the Berlekamp factorization method follows, together with
+ both the linear and quadratic varieties of the Hensel Lemma. In
+ addition there is a short section on the factorization of polynomials
+ in several variables. In general the high standard of the book is
+ maintained, but, unusually, the treatment of the modular gcd suffers a
+ little from typos and the explanation of the Hensel Lemma could be
+ clearer in places.
+
+ The major part of the final chapter is devoted to symbolic integration
+ and related topics concerning the formal solution of some ordinary
+ differential equations. These form the ‘high point’ of the book. Here
+ in particular the reader is led to the borders of current
+ research. The final part of Chapter 5 is concerned with asymptotic
+ expansions of solutions of differential equations. I found the
+ treatment of this topic too brief to be entirely successful. Those
+ already familiar with the theory of asymptotic expansion will no doubt
+ be interested in the details of the implementation, but the beginner
+ needs a fuller treatment, which this important topic surely deserves.
+
+ The book also contains an appendix and an annex. The former is
+ entitled ``Algebraic Background''. It is useful to refer to, but would
+ not be sufficient for anyone whose background did not already include
+ a fair familiarity with most of its contents. The annex contains a
+ description of the REDUCE system. Here the reader is able to see how
+ some of the algorithms described in the main part of the book are used
+ in an actual system.
+
+ The bibliography is excellent, though I do have two minor carps. One
+ or two articles mentioned in the text do not appear in the
+ bibliography, Also inclusion of one or two ‘standard’ mathematical
+ works, and appropriate reference to them in the text, would make the
+ book more accessible to people whose main speciality is not
+ Mathematics.
+
+ The few minor quibbles I have with this book are of little
+ importance. It provides an excellent introduction to Computer
+ Algebra. At the time of writing, it is still, to the best of my
+ knowledge, the only general textbook on the subject and it is indeed
+ fortunate that it is such a good one.
+
+ The second edition incorporates many recent advances in theory and
+ practice of computer algebra (a short proof of the convergence of
+ Buchberger’s algorithm as well as recent releases of software
+ described in the text). Further a description of the AXIOM system is
+ included.
+
+ This book definitely represents one of the best introductions to
+ computer algebra accessible to beginners and researchers."
+}
\end{chunk}
@@ 14156,6 +14366,22 @@ May 1984
\end{chunk}
\index{Davenport, James H.}
+\begin{chunk}{axiom.bib}
+@article{Dave11,
+ author = "Davenport, James H.",
+ title = "CICM 2011: Conferences on Intelligent Computer Mathematics 2011",
+ journal = "Springer Lecture Notes in Artificial Intelligence 6824",
+ pages = "167",
+ url = "http://people.bath.ac.uk/masjhd/Meetings/CICM2011.pdf",
+ keywords = "axiomref",
+ comment = "http://www.springerlink.com/conten/9783642226724",
+ year = "2011",
+ paper = "Dave11.pdf"
+}
+
+\end{chunk}
+
+\index{Davenport, James H.}
\begin{chunk}{ignore}
@misc{Dave12a,
author = "Davenport, James H.",
@@ 15238,7 +15464,7 @@ In Watanabe and Nagata [WN90], pp6067 ISBN 0897914015 LCCN QA76.95.I57 1990
\index{Faug\'ere, J.C.}
\index{Gianni, P.}
\index{Lazard, D.}
+\index{Lazard, Daniel}
\index{Mora, T.}
\begin{chunk}{axiom.bib}
@article{Faug94,
@@ 15589,11 +15815,99 @@ CODEN JSYCEH ISSN 07477171
@book{Gedd92,
author = "Geddes, Keith and Czapor, O. and Stephen R. and Labahn, George",
title = "Algorithms For Computer Algebra",
+ year = "1992",
publisher = "Kluwer Academic Publishers",
isbn = "0792392590",
month = "September",
year = "1992",
 keywords = "axiomref"
+ keywords = "axiomref",
+ abstract =
+ "Computer Algebra (CA) is the name given to the discipline of
+ algebraic, rather than numerical, computation. There are a number of
+ computer programs – Computer Algebra Systems (CASs) – available for
+ doing this. The most widely used generalpurpose systems that are
+ currently available commercially are Axiom, Derive, Macsyma, Maple,
+ Mathematica and REDUCE. The discipline of computer algebra began in
+ the early 1960s and the first version of REDUCE appeared in 1968.
+
+ A large class of mathematical problems can be solved by using a CAS
+ purely interactively, guided only by the user documentation. However,
+ sophisticated use requires an understanding of the considerable amount
+ of theory behind computer algebra, which in itself is an interesting
+ area of constructive mathematics. For example, most systems provide
+ some kind of programming language that allows the user to expand or
+ modify the capabilities of the system.
+
+ This book is probably the most general introduction to the theory of
+ computer algebra that is written as a textbook that develops the
+ subject through a smooth progression of topics. It describes not only
+ the algorithms but also the mathematics that underlies them. The book
+ provides an excellent starting point for the reader new to the
+ subject, and would make an excellent text for a postgraduate or
+ advanced undergraduate course. It is probably desirable for the reader
+ to have some background in abstract algebra, algorithms and
+ programming at about secondyear undergraduate level.
+
+ The book introduces the necessary mathematical background as it is
+ required for the algorithms. The authors have avoided the temptation
+ to pursue mathematics for its own sake, and it is all sharply focused
+ on the task of performing algebraic computation. The algorithms are
+ presented in a pseudolanguage that resembles a cross between Maple
+ and C. They provide a good basis for actual implementations although
+ quite a lot of work would still be required in most cases. There are
+ no code examples in any actual programming language except in the
+ introduction.
+
+ The authors are all associated with the group that began the
+ development of Maple. Hence, the book reflects the approach taken by
+ Maple, but the majority of the discussion is completely independent of
+ any actual system. The authors’ experience in implementing a practical
+ CAS comes across clearly.
+
+ The book focuses on the core of computer algebra. The first chapter
+ introduces the general concept and provides a very nice historical
+ survey. The next three chapters discuss the fundamental topics – data
+ structures, representations and the basic arithmetic of integers,
+ rational numbers, multivariate polynomials and rational functions – on
+ which the rest of the book is built.
+
+ A major technique in CA involves projection onto one or more
+ homomorphic images, for which the ground ring is usually chosen to be
+ a finite field. The image solution is lifted back to the original
+ problem domain by means of the Chinese Remainder Theorem in the case
+ of multiple homomorphic images, or the Hensel (adic or idealadic)
+ construction in the case of a single image. The next two chapters are
+ devoted to these techniques in a fairly general setting. The two
+ subsequent chapters specialise them to GCD computation and
+ factorisation for multivariate polynomials; the first of these
+ chapters also discusses the important but difficult topic of
+ subresultants.
+
+ The next two chapters describe the use of fractionfree Gaussian
+ elimination, resultants and Gröbner Bases for manipulation and exact
+ solution of linear and nonlinear polynomial equations. The two final
+ chapters describe ``classical'' algorithms and the more recent Risch
+ algorithm for symbolic indefinite integration, and provide an
+ introduction to differential algebra.
+
+ The book does not consider more specialised problem areas such as
+ symbolic summation, definite integration, differential equations,
+ group theory or number theory. Nor does it consider more applied
+ problem areas such as vectors, tensors, differential forms, special
+ functions, geometry or statistics, even though Maple and other CASs
+ provide facilities in all or many of these areas. It does not consider
+ questions of CA programming language design, nor any of the important
+ but nonalgebraic facilities provided by current CASs such as their
+ user interfaces, numerical and graphical facilities.
+
+ This is a long book (nearly 600 pages); it is generally very well
+ presented and the three authors have merged their contributions
+ seamlessly. I noticed very few typographical errors, and none of any
+ consequence. I have only two complaints about the book. The typeface
+ is too small, particularly for the relatively large line spacing used,
+ and it is much too expensive, particularly for a book that would
+ otherwise be an excellent student text. I recommend it highly to
+ anyone who can afford it."
}
\end{chunk}
@@ 16104,6 +16418,40 @@ in [Wit87], pp58
\end{chunk}
+\index{Heck, Andre}
+\begin{chunk}{axiom.bib}
+@book{Heck93,
+ author = "Heck, Andre",
+ title = "Introduction to Maple",
+ year = "1993",
+ publisher = "SpringerVerlag",
+ keywords = "axiomref",
+ abstract =
+ "This is an introductory book on one of the most powerful computer
+ algebra systems, viz, Maple: The primary emphasis in this book is on
+ learning those things that can be done with Maple and how it can be
+ used to solve mathematical problems. In this book usage of Maple as a
+ programming language is not discussed at a higher level than that of
+ defining simple procedures and using simple language constructs.
+ However, the Maple data structures are discussed in detail.
+
+ This book is divided into eighteen chapters spanning a variety of
+ topics. Starting with an introduction to symbolic computation and
+ other similar computer algebra systems, this book covers several
+ topics like polynomials and rational functions, series,
+ differentiation and integration, differential equations, linear
+ algebra, 2D and 3D graphics, etc. The applications covered include
+ kinematics of the Stanford manipulator, a 3component model for
+ cadmium transfer through the human body, molecularorbital Hückel
+ theory, prolate spheroidal coordinates and MoorePenrose inverses.
+
+ At the end of each chapter, a good number of excercises is given. A
+ list of relevant references is also given at the end of the book.
+ This book is very useful to all users of Maple package."
+}
+
+\end{chunk}
+
\index{Heck, Andrew}
\begin{chunk}{ignore}
\bibitem[Heck 01]{Hec01} Heck, A.
@@ 16690,7 +17038,7 @@ Developments. LIFL Univ. Lille, Lille France, 1993
\begin{chunk}{axiom.bib}
@article{Jaes93,
author = "Jaeschke, Gerhard",
 title = "On String Pseudoprimes to Several Bases",
+ title = "On Strong Pseudoprimes to Several Bases",
journal = "Mathematics of Computation",
volume = "61",
number = "204",
@@ 16935,6 +17283,8 @@ In Golden and Hussain [GH84], pp409??
keywords = "axiomref"
}
+\end{chunk}
+
\begin{chunk}{axiom.bib}
@misc{Acad16,
author = "Academic Search",
@@ 18202,6 +18552,29 @@ CODEN JSYCEH ISSN 07477171
\end{chunk}
+\index{Lazard, Daniel}
+\begin{chunk}{axiom.bib}
+@InProceedings{Laza93,
+ author = "Lazard, Daniel",
+ title = "On the representation of rigidbody motions and its application
+ to generalized platform manipulators",
+ booktitle = "Proc. Workshop Computational Kinematics",
+ year = "1993",
+ location = "Dagstuhl Castle, Germany",
+ publisher = "Kluwer Academic Publishers",
+ pages = "175181",
+ keywords = "axiomref",
+ abstract =
+ "Different ways for representing rigid body motions (direct isometries)
+ by a computer are presented. It turns out that the choice between them
+ may have a dramatic effect on the difficulty of a computation or of a
+ proof. As an application, a computational proof is given of the fact
+ that the direct kinematic problem for the generalized Stewart platform
+ has at most 40 complex solutions."
+}
+
+\end{chunk}
+
\index{Lebedev, Yuri}
\begin{chunk}{ignore}
\bibitem[Lebedev 08]{Leb08} Lebedev, Yuri
@@ 18728,18 +19101,6 @@ CODEN AJPIAS ISSN 00029505
\end{chunk}
\index{Page, Bill}
\begin{chunk}{axiom.bib}
@misc{Page08,
 author = "Page, Bill",
 title = "Algebraist Network",
 url = "http://lambdatheultimate.org/node/2737",
 year = "2008",
 keywords = "axiomref"
}

\end{chunk}

\subsection{M} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Mahboubi, Assia}
@@ 18963,6 +19324,36 @@ SpringerVerlag, Berlin, Germany / Heildelberg, Germany / London, UK / etc.,
\end{chunk}
+\index{Mishra, Bhubaneswar}
+\begin{chunk}{axiom.bib}
+@book{Mish93,
+ author = "Mishra, Bhubaneswar",
+ title = "Algorithmic Algebra",
+ publisher = "SpringerVerlag",
+ series = "Texts and Monographs in Computer Sciences",
+ year = "1993",
+ keywords = "axiomref",
+ abstract =
+ "This book is based on a graduate course in computer science taught in
+ 1987. The following topics are covered: computational ideal theory,
+ solving systems of polynomial equations, elimination theory, real
+ algebra, as well as an introduction chapter and two chapters with the
+ needed algebraic background. The book is selfcontained and the proofs
+ are given with many details.
+
+ It is clear that this book is only an introduction to the topic and
+ does not cover the many improvements that appeared in the last 7 years
+ about for example the computation of Groebner basis, polynomial
+ solving, multivariate resultants and algorithms in real
+ algebra. Choices had to be made to keep the content of a reasonable
+ size and the complexity issues are not considered.
+
+ The choice of topics is excellent, there are many exercises and
+ examples. It is a very useful book."
+}
+
+\end{chunk}
+
\index{Missura, Stephan A.}
\begin{chunk}{axiom.bib}
@InProceedings{Miss05,
@@ 19495,6 +19886,18 @@ interactive computing, Brunel University, Uxbridge, England, 47 September
\end{chunk}
+\index{Page, Bill}
+\begin{chunk}{axiom.bib}
+@misc{Page08,
+ author = "Page, Bill",
+ title = "Algebraist Network",
+ url = "http://lambdatheultimate.org/node/2737",
+ year = "2008",
+ keywords = "axiomref"
+}
+
+\end{chunk}
+
\index{Paule, Peter}
\index{Kartashova, Lena}
\index{Kauers, Manuel}
@@ 20104,6 +20507,60 @@ April 1991 CODEN SIGSBZ ISSN 01635824
\end{chunk}
+\index{Scheerhorn, Alfred}
+\begin{chunk}{axiom.bib}
+@misc{Sche93,
+ author = "Scheerhorn, Alfred",
+ title = "Presentation of the algebraic closure of finite fields and
+ tracecompatible polynomial sequences",
+ comment = "Darstellungen des algebraischen Abschlusses endlicher Korper
+ und spurkompatible Polynomfolgen",
+ year = "1993",
+ keywords = "axiomref",
+ abstract =
+ "For numerical experiments concerning various problems in a finite
+ field $\mathbb{F}_q$ it is useful to have an explicit data
+ presentation $\mathbb{F}_{q^m}$ of for large $m$, and a method for the
+ construction of towers
+ \[\mathbb{F}_q \subset \mathbb{F}_{q^{d_1}} \subset \cdots \subset
+ \mathbb{F}_{q^{d_k}} = \mathbb{F}_{q^m}\]
+ In order to avoid the identification problem it is advantageous to
+ have all fields in the tower presented by properly chosen normal bases,
+ whereby the embedding
+ $\mathbb{F}_{q^{d_i}} \subset \mathbb{F}_{q^{d_{i+1}}}$
+ is given by the trace function.
+
+ The following notion is introduced: A sequence of polynomials
+ $\{f_n  n \ge 1\}$ with degree$(f_n)=n$ called tracecompatible over
+ $\mathbb{F}_q$ if (1) $f_n$ is a normal polynomial over $\mathbb{F}_q$,
+ (2) if $\alpha_n \in \mathbb{F}_{q^n}$ is a root of $f_n$, then for any
+ proper divisor $d$ of $n$ the trace of $\alpha_n$ over $\mathbb{F}_{q^d}$
+ is a root of $f_d$.
+
+ The main goal of the dissertation is to give algorithms for
+ construction of sequences of tracecompatible polynomials and to
+ present explicit numerical data. An analogous notion of
+ normcompatible sequences is also introduced and studied.
+
+ The dissertation consists of four chapters and a supplement, as
+ follows: (1) Basic notions (131). (2) Presentation of the algebraic
+ closure of a finite field (3259). (3) Sequences of polynomials and
+ sequences of elements (60115). (4) Implementations (118139). (5)
+ Supplement (142171).
+
+ In chapters (1)–(3) various known results and algorithms are
+ collected, and new results are added and compared with those
+ previously used.
+
+ The numerical results in the supplement contain sequences of
+ tracecompatible polynomials of degree $n$, where $n \le 100$, and
+ $q=2,3,5,7,11,13$. For implementation, the computeralgebra system
+ AXIOM has been used. The details contained in this dissertation are
+ not readily describable in a short review."
+}
+
+\end{chunk}
+
\index{Sch\"u, J.}
\begin{chunk}{ignore}
\bibitem[Schu 92]{Sch92} Sch\"u, J.
@@ 20387,6 +20844,73 @@ Oct.Dec. 1988 CODEN JSYCEH ISSN 07477171
\end{chunk}
+\index{Singer, Michael F.}
+\index{Ulmer, Felix}
+\begin{chunk}{axiom.bib}
+@article{Sing93,
+ author = "Singer, Michael F. and Ulmer, Felix",
+ title = "Galois groups of second and third order linear differential
+ equations",
+ journal = "J. Symb. Comput.",
+ volume = "16",
+ number = "1",
+ pages = "936",
+ year = "1993",
+ keywords = "axiomref",
+ paper = "Sing93.pdf",
+ abstract =
+ "The authors discuss the first problem of Galois theory of differential
+ equations. Let $F$ be an ordinary (for simplicity) differential field
+ and $L(y)=0$ be an ordinary linear differential equation over $F$. How
+ can one calculate the Galois group of $L$ over $F$? The authors
+ suppose a new approach to the problem. They reduce it to the problem
+ of finding solutions of linear differential equations in $F$ and to
+ the factorization problem of such equations over $F$. These allow them
+ to give simple necessary and sufficient conditions for a second order
+ linear differential equation to have Liouvillian solutions and for a
+ third order linear differential equation to have Liouvillian solutions
+ or to be solvable in terms of second order equations."
+}
+
+\end{chunk}
+
+\index{Singer, Michael F.}
+\index{Ulmer, Felix}
+\begin{chunk}{axiom.bib}
+@article{Sing93a,
+ author = "Singer, Michael F. and Ulmer, Felix",
+ title = "Liouvillian and algebraic solutions of second and third order
+ linear differential equations",
+ journal = "J. Symb. Comput.",
+ volume = "16",
+ number = "1",
+ pages = "3773",
+ year = "1993",
+ paper = "Sing93a.pdf",
+ keywords = "axiomref",
+ abstract =
+ "Let $F$ be an ordinary differential field of characteristic 0 and
+ $L \in F $ be a linear homogeneous polynomial. How can one find the
+ Liouvillian solutions of $L(y)=0$? In the paper this problem is
+ reduced to the problems of (1) factorization and (2) finding $u$
+ solutions such that $\frac{u^{\prime}}{y} \in F$ of $L$ and some
+ polynomials associated with it (symmetric powers of $L$).
+
+ Now there are the algorithms for the solution of the last problems for
+ $F=\mathbb{Q}(x)$ [see D. Yu. Grigor’ev, J. Symb. Comput. 10, 737
+ (1990; Zbl 0728.68067) and M. F. Singer, Am. J. Math. 103, 661682
+ (1981; Zbl 0477.12026)].
+
+ For polynomials $L$ of the second and third order the authors provide
+ full investigation of the most difficult case when the solution $u$ of
+ $L(y)$ is algebraic. They show that one can compute the minimal
+ polynomial $P(y) \in F[y]$ of $u$. We note that the authors
+ essentially used the tools of representation theory, invariant theory
+ and computer algebra."
+}
+
+\end{chunk}
+
\index{Sit, William Y.}
\begin{chunk}{ignore}
\bibitem[Sit 89]{Sit89} Sit, W.Y.
@@ 20444,6 +20968,27 @@ LCCN QA76.76.A65 S95 1992
\end{chunk}
+\index{Smith, Geoff C.}
+\begin{chunk}{axiom.bib}
+@article{Smit93,
+ author = "Smith, Geoff C.",
+ title = "Group theory results with machine generated proofs",
+ journal = "An. Univ. Timis., Ser. Mat.Inform.",
+ volume = "31",
+ number = "2",
+ pages = "273280",
+ year = "1993",
+ keywords = "axiomref",
+ abstract =
+ "There are a variety of theorems in group theory which admit of proofs
+ by machine. This talk illustrates these techniques in action. Examples
+ are given of this phenomenon, drawn from the theory of group
+ presentations, and from the theory of $p$groups. The systems involved
+ include AXIOM, CAYLEY and QUOTPIC"
+}
+
+\end{chunk}
+
\index{Smith, Jacob}
\index{Dos Reis, Gabriel}
\index{Jarvi, Jaakko}
@@ 20537,7 +21082,17 @@ LCCN QA76.76.A65 S95 1992
publisher = "Kluwer",
url =
"http://www.iks.kti.edu/fileadmin/User/calmet/papers/Acireale93.ps.gz",
 keywords = "axiomref"
+ keywords = "axiomref",
+ paper = "Schu92.pdf",
+ abstract =
+ "The authors recall the concepts of involutive nonlinear systems of
+ partial differential equations, the classical CartanRiquierJanet
+ criterion for involutiveness, and the CartanKuranishi prolongation
+ theorem. Then the algorithm of prolongation into involutive case is
+ clearly outlined, the arising computational problems are discussed,
+ experience with implementation in the computer algebra system AXIOM
+ (1992) is described, and comparison with Maple and REDUCE algorithms
+ is made."
}
\end{chunk}
@@ 21461,6 +22016,7 @@ IBM T. J. Watson Research Center (2001)
title = "Algorithms for Type Inference with Coercions",
booktitle = "Proc ISSAC 94",
series = "ISSAC 94",
+ pages = "324329",
year = "1994",
keywords = "axiomref",
paper = "Webe94.pdf",
@@ 21842,6 +22398,8 @@ Software Preservation Group
algebra = "\newline\refto{package DFSFUN DoubleFloatSpecialFunctions}"
}
+\end{chunk}
+
\subsection{Y} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{Yap, Chee Keng}
@@ 24246,6 +24804,16 @@ Comput. J. 9 281285. (1966)
\end{chunk}
+\index{Joyner, W. D.}
+@misc{Joyn08a,
+ author = "Joyner, W. D.",
+ title = "Open Source Mathematical Software: A White Paper",
+ url = "http://wdjoyner.com/writing/research/oscasnsfwhitepaper12.tex",
+ paper = "Joyn08a.tex",
+ keywords = "axiomref",
+ year = "2008"
+}
+
\subsection{K} %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\index{TriangularSetCategory}
@@ 24306,6 +24874,19 @@ Springer Verlag Heidelberg, 1989, ISBN 0387969802
\end{chunk}
+\index{Karpinski, Stefan}
+\begin{chunk}{axiom.bib}
+@misc{Karp14,
+ author = "Karpinski, Stefan",
+ title = "Re: Symbolic Math: try a translation of Axiom to Julia?",
+ url =
+ "https://groups.google.com/forum/#!msg/juliadev/NTfS9fJuIcE/MINQuQuGfoUJ",
+ keywords = "axiomref",
+ year = "2016"
+}
+
+\end{chunk}
+
\index{Kaufmann, Matt}
\index{Manolios, Panagiotis}
\begin{chunk}{ignore}
diff git a/changelog b/changelog
index 5107e24..627fd33 100644
 a/changelog
+++ b/changelog
@@ 1,3 +1,5 @@
+20160704 tpd src/axiomwebsite/patches.html 20160706.02.tpd.patch
+20160705 tpd books/bookvolbib Axiom Citations in the Literature
20160704 tpd src/axiomwebsite/patches.html 20160706.01.tpd.patch
20160705 tpd books/bookvolbib Axiom Citations in the Literature
20160704 tpd src/axiomwebsite/patches.html 20160705.01.tpd.patch
diff git a/patch b/patch
index 6639aab..663499d 100644
 a/patch
+++ b/patch
@@ 2,397 +2,588 @@ books/bookvolbib Axiom Citations in the Literature
Goal: Axiom Literate Programming
\index{Johnson, M.E.}
\index{Rogers, C.}
\index{Schief, W.K.}
\index{Seiler, W.M.}
+index{Caruso, Fabrizio}
\begin{chunk}{axiom.bib}
@article{John94,
 author = "Johnson, M.E. and Rogers, C. and Schief, W.K. and Seiler, W.M.",
 title = "On moving pseudospherical surfaces: a generalised Weingarten
 system and its formal analysis",
 journal = "Lie Groups Appl.",
 volume = "1",
 pages = "124136",
 year = "1994",
+@misc{Caru10,
+ author = "Caruso, Fabrizio",
+ title = "Factorization of NonCommutative Polynomials",
+ url = "https://arxiv.org/pdf/1002.3108.pdf",
+ paper = "Caru10.pdf",
keywords = "axiomref",
+ year = "2010",
abstract =
 "The connection between the motion of certain curves in $\mathbb{R}^3$
 and $1+1$dimensional soliton equations is by now wellestablished. On the
 other hand, the sineGordon and other integrable equations may be
 readily derived via the classical geometry of stationary
 pseudospherical surfaces. Here, the motion of pseudospherical surfaces
 $S$ is considered in a natural orthonormal triad formulation. In one case,
 in a motion in which the Gaussian curvature of $S$ remains constant in
 time, an integrable nonlinear evolution equation is derived which has
 its origin in the description of wave propagation in an anharmonic
 crystal. In a second case, wherein the Gaussian curvature is allowed
 to vary in time, a classical generalised Weingarten system is derived
 in connection with the purely normal propagation of a pseudospherical
 surface. This is linked to triply orthogonal coordinate systems of
 Bianchi type. The generalised Weingarten system incorporates an
 integrable $2+1$dimensional sineGordon equation. The arbitrariness of the
 solutions of the generalised Weingarten system is determined via a
 completion procedure."
+ "We describe an algorithm for the factorization of noncommutative
+ polynomials over a field. The first sketch of this algorithm appeared
+ in an unpublished manuscript (literally hand written notes) by James
+ H. Davenport more than 20 years ago. This version of the algorithm
+ contains some improvements with respect to the original sketch. An
+ improved version of the algorithm has been fully implemented in the
+ Axiom computer algebra system."
}
\end{chunk}
\index{Kajler, Norbert}
\index{Soiffer, Neil}
+\index{Chen, Changbo}
+\index{Davenport, James H.}
+\index{May, John P.}
+\index{Maza, Marc Moreno}
+\index{Xia, Bican}
+\index{Xiao, Rong}
\begin{chunk}{axiom.bib}
 author = "Kajler, Norbert and Soiffer, Neil",
 title = "Some human interaction issues in computer algebra",
 journal = "SIGSAM Bulletin",
 volume = "28",
 number = "1",
 pages = "1828",
 year = "1994",
+@misc{Chen10,
+ author = "Chen, Changbo and Davenport, James H. and May, John P. and
+ Maza, Marc Moreno and Xia, Bican and Xiao, Rong",
+ title = "Triangular Decomposition of Semialgebraic Systems",
+ year = "2010",
+ url = "https://arxiv.org/pdf/1002.4784.pdf",
+ paper = "Chen10.pdf",
abstract =
 "This paper addresses some of the current issues concerning the
 improvement of user interfaces for computer algebra systems. Some
 state of the art commercial software as well as research prototypes
 are presented, followed by a description of present research
 directions."
+ "Regular chains and triangular decompositions are fundamental and
+ welldeveloped tools for describing the complex solutions of
+ polynomial systems. This paper proposes adaptations of these tools
+ focusing on solutions of the real analogue: semialgebraic systems.
+
+ We show that any such system can be decomposed into finitely many
+ regular semialgebraic systems. We propose two specifications of such
+ a decomposition and present corresponding algorithms. Under some
+ assumptions, one type of decomposition can be computed in singly
+ exponential time w.r.t. the number of variables. We implement our
+ algorithms and the experimental results illustrate their
+ effectiveness."
}
\end{chunk}
\index{Kripfganz, Jochen}
\index{Perlt, Holger}
+\index{Certik, Ondrej}
\begin{chunk}{axiom.bib}
@misc{Krip94,
 author = "Kripfganz, Jochen and Perlt, Holger",
 title = "Working with Mathematica. An Introduction with examples",
 comment = "Arbeiten mit Mathematica. Eine Einfuhrung mit Beispielen",
 book = "Hander",
 year = "1994",
+@misc{Cert16,
+ author = "Certik, Ondrej",
+ title = "SymPy vs. Axiom",
+ url = "https://github.com/sympy/sympy/wiki/SymPyvs.Axiom",
keywords = "axiomref"
}
\end{chunk}
\index{Schwarz, Fritz}
+\index{Baker, Martin}
\begin{chunk}{axiom.bib}
@InProceedings{Schw94,
 author = "Schwarz, Fritz",
 title = "Computer algebra software for scientific applications",
 booktitle = "Computerized symbolic manipulation in mechanics",
 year = "1994",
 publisher = "SpringerVerlag",
 pages = "67117",
 series = "CISM Courses Lecture 343",
+@misc{Bake16a,
+ author = "Baker, Martin",
+ title = "Axioms in Axiom",
keywords = "axiomref",
 abstract =
 "The central subject of this article are two basic questions: How to
 make the process of developing computer algebra software on a large
 scale ($10^4 to $10^5$) lines of code or more) more efficient and
 how to improve the quality of the result. Taking procedures from well
 established engineering sciences as a guide, two fundamental
 principles turned out to be of overwhelming importance: Modularization
 and limitation of growth through reuse. Important means for achieving
 these goals turned out to be concept of an abstract data type and the
 principles of objectoriented design. It is advocated to install an
 additional abstraction level between the mathematics and the machine
 in order to render it possible to develop (computer algebra) system
 independent mathematical software. Basic constituents of this level
 are a type system and a highlevel language."
+ year = "2016",
+ url = "http://www.euclideanspace.com/prog/scratchpad/axiomsinAxiom"
}
\end{chunk}
\index{Kajler, Norbert}
+\index{Joyner, W. D.}
+@misc{Joyn08,
+ author = "Joyner, W. D.",
+ title = "Open Source Mathematical Software: A White Paper",
+ url = "http://wdjoyner.com/writing/research/oscasnsfwhitepaper12.tex",
+ paper = "Joyn08.tex",
+ keywords = "axiomref",
+ year = "2008"
+}
+
+\index{Karpinski, Stefan}
\begin{chunk}{axiom.bib}
@article{Kajl92,
 author = "Kajler, Norbert",
 title = "CAS/PI: a Portable and Extensible Interface for Computer
 Algebra Systems",
 year = "1992",
 booktitle = "Proc. ISSAC 1992",
 series = "ISSAC 1992",
 pages = "376386",
 isbn = "0897914899 (soft cover) 0897914902 (hard cover)",
+@misc{Karp14,
+ author = "Karpinski, Stefan",
+ title = "Re: Symbolic Math: try a translation of Axiom to Julia?",
+ url =
+ "https://groups.google.com/forum/#!msg/juliadev/NTfS9fJuIcE/MINQuQuGfoUJ",
keywords = "axiomref",
 paper = "Kajl92.pdf",
 abstract =
 "CAS/$\pi$ is a Computer Algebra System graphic user interface
 designed to be highly portable and extensible. It has been developed
 by composition of preexisting software tools such as Maple, Sisyphe,
 or Ulysse systems, ZicVis 3D plotting library, etc, using control
 integration technology and a set of high level graphic toolkits to
 build the formula editor and the dialog manager. The main aim of
 CAS/$\pi$ is to allow a wide range of runtime recon gurations and
 extensions. For instance, it is possible to add new tools to a running
 system, to modify connections between working tools, to extend the set
 of graphic symbols managed by the formula editor, to design new high
 level editing commands based on the syntax or semantics of
 mathematical formulas, to customize and extend the menubutton based
 user interface, etc. More generally, CAS/$\pi$ can be seen equally as
 a powerful systemindependent graphic user interface enabling
 intersystems communications, a toolkit to allow fast development of
 custommade scientific software environments, or a very convenient
 framework for experimenting with computer algebra systems protocols
 and manmachine interfaces."
+ year = "2016"
}
\end{chunk}
\index{Schu, J.}
\index{Seiler, Werner Markus}
\index{Calmet, Jacques}
\begin{chunk}{axiom.bib}
@InProceedings{Schu92,
 author = "Schu, J. and Seiler, Werner Markus and Calmet, Jacques",
 title = "Algorithmic Methods For Lie Pseudogroups'",
 booktitle = "Proc. Modern Group Analysis: Advanced Analytical and
 Computational Methods in Mathematical Physics",
 pages = "337344",
 location = "Acireale (Italy)",
 year = "1992",
 publisher = "Kluwer",
 url =
 "http://www.iks.kti.edu/fileadmin/User/calmet/papers/Acireale93.ps.gz",
 keywords = "axiomref"
+@misc{America,
+ author = "america.pink",
+ title = "Axiom (computer algebra system)",
+ year = "2016",
+ keywords = "axiomref",
+ url = "http://america.pink/axiomcomputeralgebrasystem_526647.html"
}
\end{chunk}
\index{Seiler, Werner Markus}
+\index{Davenport, James H.}
+\index{Siret, Y.}
+\index{Tournier, E.}
\begin{chunk}{axiom.bib}
@article{Seil99,
 author = "Seiler, Werner Markus",
 title = "DETools: A Library for Differential Equations",
 paper = "Seil99.pdf",
 year = "1999",
+@book{Dave88,
+ author = "Davenport, James H. and Siret, Y. and Tournier, E.",
+ title =
+ "Computer Algebra: Systems and Algorithms for Algebraic Computation",
+ publisher = "Academic Press",
+ year = "1988",
+ isbn ="0122042329",
+ url = "http://staff.bath.ac.uk/masjhd/masternew.pdf",
+ paper = "Dave88.pdf",
keywords = "axiomref",
abstract =
 "This article tries to give at least a brief introduction. The MuPAD
 library is extended on two levels. The first one consists of a new
 library detools containing a number of routines for treating
 differential equations. This includes support for the graphical
 presentation of the output of the numerical routines in MuPAD, some
 methods for analysing or generating differential equations and also
 routines for solving some classes of partial differential
 equations. The use of this new library will be described in this
 article. The second level is somewhat more advanced and requires a
 certain familiarity with the objectoriented domains."
+ "The need for a good general text on Computer Algebra has never been
+ greater. From the very beginning, computers have been used for
+ numerical calculation. It is not always realized however that their
+ use for mathematical calculation of a symbolic nature has a history
+ almost as long. It is only recently that improvement in algorithms,
+ the development of small systems and the emergence of powerful
+ workstations have combined to make Computer Algebra systems much more
+ widely available and an increasingly important tool for almost all
+ users of Mathematics. Part of the reason why Computer Algebra was for
+ so long something of an esoteric discipline, has surely been the lack
+ of textbooks on the subject. The arrival of the present volume on the
+ scene has thus been particularly fortunate.
+
+ The approach adopted by the authors is to begin by giving the reader
+ an idea of the sort of calculations that Algebra Systems can
+ perform. Next the questions of data representation are
+ treated. Finally the bulk of the book is devoted to explaining the
+ classical algorithms of the subject. The reader is thereby given both
+ a feel for the problems, such as data representation and combinatorial
+ explosion, that system designers need to face, and a general
+ understanding of the underlying Mathematics. The book is not intended
+ to provide encyclopedic coverage, nor is it meant to be serve as a
+ manual for any particular system.
+
+ One of the more difficult design decisions facing authors of such a
+ book concerns the level of mathematical sophistication to be assumed
+ on behalf of the reader. One wants the book to be accessible to as
+ wide an audience as possible, but any understanding of the subject
+ beyond the more superficial requires a reasonable grasp of the
+ underlying Pure Mathematics. The compromise made in the present text
+ is to fully explain the mathematical problems, to state the theorems
+ and consequent algorithms, but not always to prove the theorems. Many
+ of the more straightforward results are proved though. The decisions
+ as to what to include and what to omit have been well thought out and
+ the result is a considerable success. The book has a great deal to
+ offer engineers and scientists and its early chapters in particular
+ could most suitably serve as the basis for an undergraduate
+ course. For the professional mathematician it provides a good quick
+ allround introduction to a fascinating and rapidly evolving area.
+
+ Of course in a book such as this, not everything that might fall under
+ the umbrella of Computer Algebra can be covered. Thus some specialized
+ topics, such as Computational Group Theory, are not mentioned, and the
+ treatment of other areas is sometimes necessarily abbreviated. However
+ the main stream of the subject is well represented, and the selection
+ of material generally well judged. Typically, the main classical
+ results are fully explained, some of the more interesting developments
+ and variations are sketched, and the reader is referred to the
+ standard literature of the subject for further details.
+
+ The first chapter is entitled ``How to use a Computer Algebra
+ System''. Here the reader is led through a session with the MACSYMA
+ system obtaining a vicarious handson experience. Beginners would be
+ well advised to follow the authors’ suggestion and duplicate the
+ session on their local system as closely as possible. The examples
+ chosen are interesting, though perhaps a little too ‘pure
+ mathematical’ for some tastes. Overall the chapter gives a good idea
+ of the capabilities of algebra systems.
+
+ Chapter 2 is concerned with the representation of the various
+ mathematical quantities which algebra systems handle. It might be
+ thought that data repesentation is mainly a computerscience matter,
+ but in fact some rather interesting mathematical problems concerning
+ uniqueness arise. The chapter includes, among other things, discussion
+ of the non modular methods for computing gcds (the subresultant
+ algorithm for example), the handling of algebraic quantities the Risch
+ Structure Theorem and the Bareiss Method of Gaussian elimination.
+
+ The third chapter treats two major topics under the heading
+ ``Polynomial Simplification''. Firstly there is a concise, but good,
+ explanation of Buchberger’s Groebnerbasis methods for computations in
+ polynomial rings. Secondly there is an equally good introduction to
+ the use of cylindrical decomposition for obtaining approximations to
+ real roots of polynomial equations.
+
+ Chapter 4, which is headed ``Advanced Algorithms'', begins with a
+ discussion of modular methods, in particular the modular gcd. A brisk
+ treatment of the Berlekamp factorization method follows, together with
+ both the linear and quadratic varieties of the Hensel Lemma. In
+ addition there is a short section on the factorization of polynomials
+ in several variables. In general the high standard of the book is
+ maintained, but, unusually, the treatment of the modular gcd suffers a
+ little from typos and the explanation of the Hensel Lemma could be
+ clearer in places.
+
+ The major part of the final chapter is devoted to symbolic integration
+ and related topics concerning the formal solution of some ordinary
+ differential equations. These form the ‘high point’ of the book. Here
+ in particular the reader is led to the borders of current
+ research. The final part of Chapter 5 is concerned with asymptotic
+ expansions of solutions of differential equations. I found the
+ treatment of this topic too brief to be entirely successful. Those
+ already familiar with the theory of asymptotic expansion will no doubt
+ be interested in the details of the implementation, but the beginner
+ needs a fuller treatment, which this important topic surely deserves.
+
+ The book also contains an appendix and an annex. The former is
+ entitled ``Algebraic Background''. It is useful to refer to, but would
+ not be sufficient for anyone whose background did not already include
+ a fair familiarity with most of its contents. The annex contains a
+ description of the REDUCE system. Here the reader is able to see how
+ some of the algorithms described in the main part of the book are used
+ in an actual system.
+
+ The bibliography is excellent, though I do have two minor carps. One
+ or two articles mentioned in the text do not appear in the
+ bibliography, Also inclusion of one or two ‘standard’ mathematical
+ works, and appropriate reference to them in the text, would make the
+ book more accessible to people whose main speciality is not
+ Mathematics.
+
+ The few minor quibbles I have with this book are of little
+ importance. It provides an excellent introduction to Computer
+ Algebra. At the time of writing, it is still, to the best of my
+ knowledge, the only general textbook on the subject and it is indeed
+ fortunate that it is such a good one.
+
+ The second edition incorporates many recent advances in theory and
+ practice of computer algebra (a short proof of the convergence of
+ Buchberger’s algorithm as well as recent releases of software
+ described in the text). Further a description of the AXIOM system is
+ included.
+
+ This book definitely represents one of the best introductions to
+ computer algebra accessible to beginners and researchers."
}
\end{chunk}
\index{Bradford, Russell}
\index{Davenport, James H.}
\index{England, Matthew}
\index{McCallum, Scott}
\index{Wilson, David}
+\index{Heck, Andre}
\begin{chunk}{axiom.bib}
@misc{Brad15,
 author = "Bradford, Russell and Davenport, James H. and England, Matthew and
 McCallum, Scott",
 title = "Truth Table Invariant Cylindrical Algebraic Decomposition",
 url = "https://arxiv.org/pdf/1401.0645.pdf",
 paper = "Brad15.pdf",
 year = "2015",
+@book{Heck93,
+ author = "Heck, Andre",
+ title = "Introduction to Maple",
+ year = "1993",
+ publisher = "SpringerVerlag",
+ keywords = "axiomref",
abstract =
 "When using cylindrical algebraic decomposition (CAD) to solve a
 problem with respect to a set of polynomials, it is likely not the
 signs of those polynomials that are of paramount importance but rather
 the truth values of certain quantifier free formulae involving
 them. This observation motivates our article and definition of a Truth
 Table Invariant CAD (TTICAD). In ISSAC 2013 the current authors
 presented an algorithm that can efficiently and directly construct a
 TTICAD for a list of formulae in which each has an equational
 constraint. This was achieved by generalising McCallum's theory of
 reduced projection operators. In this paper we present an extended
 version of our theory which can be applied to an arbitrary list of
 formulae, achieving savings if at least one has an equational
 constraint. We also explain how the theory of reduced projection
 operators can allow for further improvements to the lifting phase of
 CAD algorithms, even in the context of a single equational constraint.
 The algorithm is implemented fully in Maple and we present both
 promising results from experimentation and a complexity analysis
 showing the benefits of our contributions."
+ "This is an introductory book on one of the most powerful computer
+ algebra systems, viz, Maple: The primary emphasis in this book is on
+ learning those things that can be done with Maple and how it can be
+ used to solve mathematical problems. In this book usage of Maple as a
+ programming language is not discussed at a higher level than that of
+ defining simple procedures and using simple language constructs.
+ However, the Maple data structures are discussed in detail.
+
+ This book is divided into eighteen chapters spanning a variety of
+ topics. Starting with an introduction to symbolic computation and
+ other similar computer algebra systems, this book covers several
+ topics like polynomials and rational functions, series,
+ differentiation and integration, differential equations, linear
+ algebra, 2D and 3D graphics, etc. The applications covered include
+ kinematics of the Stanford manipulator, a 3component model for
+ cadmium transfer through the human body, molecularorbital Hückel
+ theory, prolate spheroidal coordinates and MoorePenrose inverses.
+
+ At the end of each chapter, a good number of excercises is given. A
+ list of relevant references is also given at the end of the book.
+ This book is very useful to all users of Maple package."
}
\end{chunk}
\index{Bradford, Russell}
\index{Chen, Changbo}
\index{Davenport, James H.}
\index{England, Matthew}
\index{Maza, Marc Moreno}
\index{Wilson, David}
+\index{Lazard, Daniel}
\begin{chunk}{axiom.bib}
@misc{Brad14,
 author = "Bradford, Russell and Chen, Changbo and Davenport, James H. and
 England, Matthew and Maza, Marc Moreno and Wilson, David",
 title = "Truth Table Invariant Cylindrical Algebraic Decomposition by
 Regular Chains",
 url = "https://arxiv.org/pdf/1401.6310.pdf",
 paper = "Brad14.pdf",
 year = "2014",
+@InProceedings{Laza93,
+ author = "Lazard, Daniel",
+ title = "On the representation of rigidbody motions and its application
+ to generalized platform manipulators",
+ booktitle = "Proc. Workshop Computational Kinematics",
+ year = "1993",
+ location = "Dagstuhl Castle, Germany",
+ publisher = "Kluwer Academic Publishers",
+ pages = "175181",
+ keywords = "axiomref",
abstract =
 "A new algorithm to compute cylindrical algebraic decompositions
 (CADs) is presented, building on two recent advances. Firstly, the
 output is truth table invariant (a TTICAD) meaning given formulae have
 constant truth value on each cell of the decomposition. Secondly, the
 computation uses regular chains theory to first build a cylindrical
 decomposition of complex space (CCD) incrementally by polynomial.
 Significant modification of the regular chains technology wa s used to
 achieve the more sophisticated invariance criteria. Experimental
 results on an implementation in the {\tt RegularChains} Library for Maple
 verify that combining these advances gives an algorithm superior to
 its individual components and competitive with the state of the art."
+ "Different ways for representing rigid body motions (direct isometries)
+ by a computer are presented. It turns out that the choice between them
+ may have a dramatic effect on the difficulty of a computation or of a
+ proof. As an application, a computational proof is given of the fact
+ that the direct kinematic problem for the generalized Stewart platform
+ has at most 40 complex solutions."
}
\end{chunk}
\index{Wilson, David}
\index{Bradford, Russell}
\index{Davenport, James H.}
\index{England, Matthew}
+\index{Mishra, Bhubaneswar}
\begin{chunk}{axiom.bib}
@misc{Wils14,
 author = "Wilson, David and Bradford, Russell and Davenport, James H. and
 England, Matthew",
 title = "Cylindrical Algebraic SubDecompositions",
 url = "https://arxiv.org/pdf/1401.0647.pdf",
 paper = "Wils14.pdf",
 year = "2014",
 abstract =
 "Cylindrical algebraic decompositions (CADs) are a key tool in real
 algebraic geometry, used primarily for eliminating quantifiers over
 the reals and studying semialgebraic sets. In this paper we
 introduce cylindrical algebraic subdecompositions (subCADs), which
 are subsets of CADs containing all the information needed to specify a
 solution for a given problem. We define two new types of subCAD:
 variety subCADs which are those cells in a CAD lying on a designated
 variety; and layered subCADs which have only those cells of
 dimension higher than a specified value. We present algorithms to
 produce these and describe how the two approaches may be combined with
 each other and the recent theory of truthtable invariant CAD. We
 give a complexity analysis showing that these techniques can offer
 substantial theoretical savings, which is supported by experimentation
 using an implementation in Maple."
+@book{Mish93,
+ author = "Mishra, Bhubaneswar",
+ title = "Algorithmic Algebra",
+ publisher = "SpringerVerlag",
+ series = "Texts and Monographs in Computer Sciences",
+ year = "1993",
+ keywords = "axiomref",
+ abstract =
+ "This book is based on a graduate course in computer science taught in
+ 1987. The following topics are covered: computational ideal theory,
+ solving systems of polynomial equations, elimination theory, real
+ algebra, as well as an introduction chapter and two chapters with the
+ needed algebraic background. The book is selfcontained and the proofs
+ are given with many details.
+
+ It is clear that this book is only an introduction to the topic and
+ does not cover the many improvements that appeared in the last 7 years
+ about for example the computation of Groebner basis, polynomial
+ solving, multivariate resultants and algorithms in real
+ algebra. Choices had to be made to keep the content of a reasonable
+ size and the complexity issues are not considered.
+
+ The choice of topics is excellent, there are many exercises and
+ examples. It is a very useful book."
}
\end{chunk}
\index{England, Matthew}
\index{Wilson, David}
\index{Bradford, Russell}
\index{Davenport, James H.}
+\index{Scheerhorn, Alfred}
\begin{chunk}{axiom.bib}
@misc{Engl14,
 author = "England, Matthew and Wilson, David and Bradford, Russell and
 Davenport, James H.",
 title = "Using the Regular Chains Library to build cylindrical algebraic
 decompositions by projecting and lifting",
 url = "https://arxiv.org/pdf/1405.6090.pdf",
 paper = "Engl14.pdf",
 year = "2014",
+@misc{Sche93,
+ author = "Scheerhorn, Alfred",
+ title = "Presentation of the algebraic closure of finite fields and
+ tracecompatible polynomial sequences",
+ comment = "Darstellungen des algebraischen Abschlusses endlicher Korper
+ und spurkompatible Polynomfolgen",
+ year = "1993",
+ keywords = "axiomref",
abstract =
 "Cylindrical algebraic decomposition (CAD) is an important tool, both
 for quantifier elimination over the reals and a range of other
 applications. Traditionally, a CAD is built through a process of
 projection and lifting to move the problem within Euclidean spaces of
 changing dimension. Recently, an alternative approach which first
 decomposes complex space using triangular decomposition before
 refining to real space has been introduced and implemented within the
 RegularChains Library of Maple. We here describe a freely available
 package ProjectionCAD which utilises the routines within the
 RegularChains Library to build CADs by projection and lifting. We
 detail how the projection and lifting algorithms were modified to
 allow this, discuss the motivation and survey the functionality of the
 package."
+ "For numerical experiments concerning various problems in a finite
+ field $\mathbb{F}_q$ it is useful to have an explicit data
+ presentation $\mathbb{F}_{q^m}$ of for large $m$, and a method for the
+ construction of towers
+ \[\mathbb{F}_q \subset \mathbb{F}_{q^{d_1}} \subset \cdots \subset
+ \mathbb{F}_{q^{d_k}} = \mathbb{F}_{q^m}\]
+ In order to avoid the identification problem it is advantageous to
+ have all fields in the tower presented by properly chosen normal bases,
+ whereby the embedding
+ $\mathbb{F}_{q^{d_i}} \subset \mathbb{F}_{q^{d_{i+1}}}$
+ is given by the trace function.
+
+ The following notion is introduced: A sequence of polynomials
+ $\{f_n  n \ge 1\}$ with degree$(f_n)=n$ called tracecompatible over
+ $\mathbb{F}_q$ if (1) $f_n$ is a normal polynomial over $\mathbb{F}_q$,
+ (2) if $\alpha_n \in \mathbb{F}_{q^n}$ is a root of $f_n$, then for any
+ proper divisor $d$ of $n$ the trace of $\alpha_n$ over $\mathbb{F}_{q^d}$
+ is a root of $f_d$.
+
+ The main goal of the dissertation is to give algorithms for
+ construction of sequences of tracecompatible polynomials and to
+ present explicit numerical data. An analogous notion of
+ normcompatible sequences is also introduced and studied.
+
+ The dissertation consists of four chapters and a supplement, as
+ follows: (1) Basic notions (131). (2) Presentation of the algebraic
+ closure of a finite field (3259). (3) Sequences of polynomials and
+ sequences of elements (60115). (4) Implementations (118139). (5)
+ Supplement (142171).
+
+ In chapters (1)–(3) various known results and algorithms are
+ collected, and new results are added and compared with those
+ previously used.
+
+ The numerical results in the supplement contain sequences of
+ tracecompatible polynomials of degree $n$, where $n \le 100$, and
+ $q=2,3,5,7,11,13$. For implementation, the computeralgebra system
+ AXIOM has been used. The details contained in this dissertation are
+ not readily describable in a short review."
}
\end{chunk}
\index{England, Matthew}
\index{Bradford, Russell}
\index{Davenport, James H.}
\index{Wilson, David}
+\index{Singer, Michael F.}
+\index{Ulmer, Felix}
+\begin{chunk}{axiom.bib}
+@article{Sing93,
+ author = "Singer, Michael F. and Ulmer, Felix",
+ title = "Galois groups of second and third order linear differential
+ equations",
+ journal = "J. Symb. Comput.",
+ volume = "16",
+ number = "1",
+ pages = "936",
+ year = "1993",
+ keywords = "axiomref",
+ paper = "Sing93.pdf",
+ abstract =
+ "The authors discuss the first problem of Galois theory of differential
+ equations. Let $F$ be an ordinary (for simplicity) differential field
+ and $L(y)=0$ be an ordinary linear differential equation over $F$. How
+ can one calculate the Galois group of $L$ over $F$? The authors
+ suppose a new approach to the problem. They reduce it to the problem
+ of finding solutions of linear differential equations in $F$ and to
+ the factorization problem of such equations over $F$. These allow them
+ to give simple necessary and sufficient conditions for a second order
+ linear differential equation to have Liouvillian solutions and for a
+ third order linear differential equation to have Liouvillian solutions
+ or to be solvable in terms of second order equations."
+}
+
+\end{chunk}
+
+\index{Singer, Michael F.}
+\index{Ulmer, Felix}
\begin{chunk}{axiom.bib}
@misc{Engl14a,
 author = "England, Matthew and Bradford, Russell and Davenport, James H. and
 Wilson, David",
 title = "Choosing a variable ordering for truthtable invariant cylindrical
 algebraic decomposition by incremental triangular decomposition",
 url = "https://arxiv.org/pdf/1405.6094.pdf",
 paper = "Engl14a.pdf",
 year = "2014",
+@article{Sing93a,
+ author = "Singer, Michael F. and Ulmer, Felix",
+ title = "Liouvillian and algebraic solutions of second and third order
+ linear differential equations",
+ journal = "J. Symb. Comput.",
+ volume = "16",
+ number = "1",
+ pages = "3773",
+ year = "1993",
+ paper = "Sing93a.pdf",
+ keywords = "axiomref",
abstract =
 "Cylindrical algebraic decomposition (CAD) is a key tool for solving
 problems in real algebraic geometry and beyond. In recent years a new
 approach has been developed, where regular chains technology is used
 to first build a decomposition in complex space. We consider the
 latest variant of this which builds the complex decomposition
 incrementally by polynomial and produces CADs on whose cells a
 sequence of formulae are truthinvariant. Like all CAD algorithms the
 user must provide a variable ordering which can have a profound impact
 on the tractability of a problem. We evaluate existing heuristics to
 help with the choice for this algorithm, suggest improvements and then
 derive a new heuristic more closely aligned with the mechanics of the
 new algorithm."
+ "Let $F$ be an ordinary differential field of characteristic 0 and
+ $L \in F $ be a linear homogeneous polynomial. How can one find the
+ Liouvillian solutions of $L(y)=0$? In the paper this problem is
+ reduced to the problems of (1) factorization and (2) finding $u$
+ solutions such that $\frac{u^{\prime}}{y} \in F$ of $L$ and some
+ polynomials associated with it (symmetric powers of $L$).
+
+ Now there are the algorithms for the solution of the last problems for
+ $F=\mathbb{Q}(x)$ [see D. Yu. Grigor’ev, J. Symb. Comput. 10, 737
+ (1990; Zbl 0728.68067) and M. F. Singer, Am. J. Math. 103, 661682
+ (1981; Zbl 0477.12026)].
+
+ For polynomials $L$ of the second and third order the authors provide
+ full investigation of the most difficult case when the solution $u$ of
+ $L(y)$ is algebraic. They show that one can compute the minimal
+ polynomial $P(y) \in F[y]$ of $u$. We note that the authors
+ essentially used the tools of representation theory, invariant theory
+ and computer algebra."
}
\end{chunk}
\index{England, Matthew}
\index{Bradford, Russell}
\index{Chen, Changbo}
\index{Davenport, James H.}
\index{Maza, Marc Moreno}
\index{Wilson, David}
+\index{Smith, Geoff C.}
\begin{chunk}{axiom.bib}
@misc{Engl14b,
 author = "England, Matthew and Bradford, Russell and Chen, Changbo and
 Davenport, James H. and Maza, Marc Moreno",
 title = "Problem formulation for truthtable invariant cylindrical
 algebraic decomposition by incremental triangular decomposition",
 url = "https://arxiv.org/pdf/1404.6371.pdf",
 paper = "Engl14b.pdf",
 year = "2014",
+@article{Smit93,
+ author = "Smith, Geoff C.",
+ title = "Group theory results with machine generated proofs",
+ journal = "An. Univ. Timis., Ser. Mat.Inform.",
+ volume = "31",
+ number = "2",
+ pages = "273280",
+ year = "1993",
+ keywords = "axiomref",
abstract =
 "Cylindrical algebraic decompositions (CADs) are a key tool for
 solving problems in real algebraic geometry and beyond. We recently
 presented a new CAD algorithm combining two advances: truthtable
 invariance, making the CAD invariant with respect to the truth of
 logical formulae rather than the signs of polynomials; and CAD
 construction by regular chains technology, where first a complex
 decomposition is constructed by refining a tree incrementally by
 constraint. We here consider how best to formulate problems for input
 to this algorithm. We focus on a choice (not relevant for other CAD
 algorithms) about the order in which constraints are presented. We
 develop new heuristics to help make this choice and thus allow the
 best use of the algorithm in practice. We also consider other choices
 of problem formulation for CAD, as discussed in CICM 2013, revisiting
 these in the context of the new algorithm."
+ "There are a variety of theorems in group theory which admit of proofs
+ by machine. This talk illustrates these techniques in action. Examples
+ are given of this phenomenon, drawn from the theory of group
+ presentations, and from the theory of $p$groups. The systems involved
+ include AXIOM, CAYLEY and QUOTPIC"
}
\end{chunk}
\index{Chen, Changbo}
\index{Maza, Marc Moreno}
+\index{Geddes, K. O.}
+\index{Czapor, S.R.}
+\index{Labahn, George}
\begin{chunk}{axiom.bib}
@misc{Chen12,
 author = "Chen, Changbo and Maza, Marc Moreno",
 title = "An Incremental Algorithm for Computing Cylindrical Algebraic
 Decompositions",
 url = "https://arxiv.org/pdf/1210.5543.pdf",
 paper = "Chen12.pdf",
 year = "2012",
+@book{Gedd92,
+ author = "Geddes, Keith and Czapor, O. and Stephen R. and Labahn, George",
+ title = "Algorithms For Computer Algebra",
+ year = "1992",
+ publisher = "Kluwer Academic Publishers",
+ isbn = "0792392590",
+ month = "September",
+ year = "1992",
+ keywords = "axiomref",
abstract =
 "In this paper, we propose an incremental algorithm for computing
 cylindrical al gebraic decompositions. The algorithm consists of two
 parts: computing a complex cylindrical tree and refining this complex
 tree into a cylindrical tree in real space. The incrementality comes
 from the first part of the algorithm, where a complex cylindrical tree
 is constructed by refining a previous complex cylindrical tree with a
 polynomial constraint. We have implemented our algorithm in Maple. The
 experimentation shows that the proposed algorithm outperforms existing
 ones for many examples taken from the literature"
+ "Computer Algebra (CA) is the name given to the discipline of
+ algebraic, rather than numerical, computation. There are a number of
+ computer programs – Computer Algebra Systems (CASs) – available for
+ doing this. The most widely used generalpurpose systems that are
+ currently available commercially are Axiom, Derive, Macsyma, Maple,
+ Mathematica and REDUCE. The discipline of computer algebra began in
+ the early 1960s and the first version of REDUCE appeared in 1968.
+
+ A large class of mathematical problems can be solved by using a CAS
+ purely interactively, guided only by the user documentation. However,
+ sophisticated use requires an understanding of the considerable amount
+ of theory behind computer algebra, which in itself is an interesting
+ area of constructive mathematics. For example, most systems provide
+ some kind of programming language that allows the user to expand or
+ modify the capabilities of the system.
+
+ This book is probably the most general introduction to the theory of
+ computer algebra that is written as a textbook that develops the
+ subject through a smooth progression of topics. It describes not only
+ the algorithms but also the mathematics that underlies them. The book
+ provides an excellent starting point for the reader new to the
+ subject, and would make an excellent text for a postgraduate or
+ advanced undergraduate course. It is probably desirable for the reader
+ to have some background in abstract algebra, algorithms and
+ programming at about secondyear undergraduate level.
+
+ The book introduces the necessary mathematical background as it is
+ required for the algorithms. The authors have avoided the temptation
+ to pursue mathematics for its own sake, and it is all sharply focused
+ on the task of performing algebraic computation. The algorithms are
+ presented in a pseudolanguage that resembles a cross between Maple
+ and C. They provide a good basis for actual implementations although
+ quite a lot of work would still be required in most cases. There are
+ no code examples in any actual programming language except in the
+ introduction.
+
+ The authors are all associated with the group that began the
+ development of Maple. Hence, the book reflects the approach taken by
+ Maple, but the majority of the discussion is completely independent of
+ any actual system. The authors’ experience in implementing a practical
+ CAS comes across clearly.
+
+ The book focuses on the core of computer algebra. The first chapter
+ introduces the general concept and provides a very nice historical
+ survey. The next three chapters discuss the fundamental topics – data
+ structures, representations and the basic arithmetic of integers,
+ rational numbers, multivariate polynomials and rational functions – on
+ which the rest of the book is built.
+
+ A major technique in CA involves projection onto one or more
+ homomorphic images, for which the ground ring is usually chosen to be
+ a finite field. The image solution is lifted back to the original
+ problem domain by means of the Chinese Remainder Theorem in the case
+ of multiple homomorphic images, or the Hensel (adic or idealadic)
+ construction in the case of a single image. The next two chapters are
+ devoted to these techniques in a fairly general setting. The two
+ subsequent chapters specialise them to GCD computation and
+ factorisation for multivariate polynomials; the first of these
+ chapters also discusses the important but difficult topic of
+ subresultants.
+
+ The next two chapters describe the use of fractionfree Gaussian
+ elimination, resultants and Gröbner Bases for manipulation and exact
+ solution of linear and nonlinear polynomial equations. The two final
+ chapters describe ``classical'' algorithms and the more recent Risch
+ algorithm for symbolic indefinite integration, and provide an
+ introduction to differential algebra.
+
+ The book does not consider more specialised problem areas such as
+ symbolic summation, definite integration, differential equations,
+ group theory or number theory. Nor does it consider more applied
+ problem areas such as vectors, tensors, differential forms, special
+ functions, geometry or statistics, even though Maple and other CASs
+ provide facilities in all or many of these areas. It does not consider
+ questions of CA programming language design, nor any of the important
+ but nonalgebraic facilities provided by current CASs such as their
+ user interfaces, numerical and graphical facilities.
+
+ This is a long book (nearly 600 pages); it is generally very well
+ presented and the three authors have merged their contributions
+ seamlessly. I noticed very few typographical errors, and none of any
+ consequence. I have only two complaints about the book. The typeface
+ is too small, particularly for the relatively large line spacing used,
+ and it is much too expensive, particularly for a book that would
+ otherwise be an excellent student text. I recommend it highly to
+ anyone who can afford it."
}
\end{chunk}
diff git a/src/axiomwebsite/patches.html b/src/axiomwebsite/patches.html
index e751a9d..e3c6295 100644
 a/src/axiomwebsite/patches.html
+++ b/src/axiomwebsite/patches.html
@@ 5456,6 +5456,8 @@ books/bookvolbib Axiom Citations in the Literature
books/bookvolbib Axiom Citations in the Literature
20160706.01.tpd.patch
books/bookvolbib Axiom Citations in the Literature
+20160706.02.tpd.patch
+books/bookvolbib Axiom Citations in the Literature

1.7.5.4